Amy paid $68.68 for a pair of running shoes during a 35 %-off sale. What was the regular price?
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Find the inverse, interchange the variables to solve for y
f-1 (x)=-![\frac{8- \sqrt[]{_2(-8+x)} }{2} ,](https://tex.z-dn.net/?f=%20%5Cfrac%7B8-%20%5Csqrt%5B%5D%7B_2%28-8%2Bx%29%7D%20%7D%7B2%7D%20%2C)
f-1 (x)=-
So first we solve for y in second equation
3x+y=4
y=4-3x
sub for y in first equiton
2x-(4-3x)^2=1
2x-(16-12x-12x+9x^2)=1
2x-(16-24x+9x^2)=1
2x-16+24x-9x^2=1
-9x^2+26x-16=1
times -1 both sides
9x^2-26x+16=-1
add 1 to both sides
9x^2-26x+17=0
factor
(x-1)(9x-17)=0
set each to zero
x-1=0
x=1
9x-17=0
9x=17
x=17/9
so sub back to find y
y=4-3x
y=4-3(1)
y=4-3
y=1
(1,1)
y=4-3x
y=4-3(17/9)
y=4-17/3
y=12/3-17/3
y=-5/3
(17/9,-5/3)
the 2 intersection points are
(1,1) and
3x+y=4
y=4-3x
sub for y in first equiton
2x-(4-3x)^2=1
2x-(16-12x-12x+9x^2)=1
2x-(16-24x+9x^2)=1
2x-16+24x-9x^2=1
-9x^2+26x-16=1
times -1 both sides
9x^2-26x+16=-1
add 1 to both sides
9x^2-26x+17=0
factor
(x-1)(9x-17)=0
set each to zero
x-1=0
x=1
9x-17=0
9x=17
x=17/9
so sub back to find y
y=4-3x
y=4-3(1)
y=4-3
y=1
(1,1)
y=4-3x
y=4-3(17/9)
y=4-17/3
y=12/3-17/3
y=-5/3
(17/9,-5/3)
the 2 intersection points are
(1,1) and